Is it correct that once I have tax card with certain amount, I cannot reduce it at all. For example: Gross income is 20000 and tax rate is ~9%. If something goes wrong then it is impossible to reduce it. Person has to pay 9% even if income goes to 12000 where tax is around 3%.

All you have to do is call or visit your local tax office, tell them how much money you've earned so far this year, how much tax (veroennakko on your most recent pay stub) you've paid so far this year, and how much money you still plan to earn this year (or alternatively, what you expect your new annual gross income to be). They'll plug the numbers into their system and give you a new tax card. You in turn have to give the new tax card to your employer so they adjust your tax rate.

If you're lucky enough to have an EEA-issued ID card and have asked your bank to grant you TUPAS permissions, you can also just log into Vero's website using your online banking ID and do this yourself.